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Determine the derivative.$$f(x)=x^{2} \mathrm{e}^{2 x}$$

$2 x e^{2 x}(x+1)$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 4

The Derivative of the Exponential Function

McMaster University

University of Michigan - Ann Arbor

Idaho State University

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Find the derivative of the…

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Find the second derivative…

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Calculate the derivative. …

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So we're asked to find the derivative of this function X squared to the two X. If you notice what we have is that we have this giant product in here. Um so when I see a product, I think of product rule and actually to the right is going to be the chain rule going Get to that piece on. That's the real meat of this lesson so well are tasked with finding the derivative, Um, that's f prime of X. What we get is a derivative of the left side, which is two X. You leave the seat to the two x alone and then plus leave X squared alone times the derivative E to the two X, which is your channel on. The derivative is itself either the two x times, the derivative of two X, which is to now some teachers will let you leave your answer like this, and other teachers will expect you to factor out because each one of these pieces has a two x e to the two x power. It's your greatest common factor, and then you'll be left with one plus. I see I took out the two I took out of the two X. I took out one of these exes, so I need one more left over. So this is an acceptable answer as well. Either one works.

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